The expression on the right-hand side of the Douglas identity comes from symmetrization of the so-called Bregman divergence [1]}. Namely, for \(p>1\)  and \(a,b\in \mathbb {R}\)  we define
\(F_p(a,b) = |b|^p - |a|^p - pa^{\langle p-1\rangle }(b-a).\) 
